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Abstract:

A plasma processing system includes a processing chamber provided with a
plasma generation unit for applying radio-frequency power to supplied
processing gas to generate plasma and a stage for holding workpieces, and
a control computer for generating plasma in accordance with preset
processing conditions to sequentially apply plasma processing to the
workpieces and also for sequentially collecting system parameter values
each of which represents a state of the plasma processing. The computer
is provided with a record unit for storing, in every predetermined
period, a frequency that each of the collected system parameter values
deviates from a preset reference value, an occurrence rate calculation
unit for calculating, based on the frequency, an occurrence rate that the
each of the system parameter values deviates from the reference value,
and a comparison unit for comparing the occurrence rate with a preset
reference value to diagnose a state of the system.

Claims:

1. A plasma processing system comprising:a processing chamber provided
with a plasma generation unit for applying radio-frequency power to
supplied processing gas to generate plasma and a stage for holding
workpieces thereon, anda control computer for generating plasma in
accordance with preset processing conditions to sequentially apply plasma
processing to the workpieces held on said stage and also for sequentially
collecting system parameter values each of which represents a state of
the plasma processing,wherein said control computer is provided with:a
record unit for storing, in every predetermined period, a frequency that
each of the collected system parameter values deviates from a preset
reference value,an occurrence rate calculation unit for calculating,
based on the frequency, an occurrence rate that the each of the system
parameter values deviates from the reference value, anda comparison unit
for comparing the occurrence rate with a preset reference value to
diagnose a state of said system.

2. A plasma processing system comprising:a processing chamber provided
with a plasma generation unit for applying radio-frequency power to
supplied processing gas to generate plasma and a stage for holding
workpieces thereon, anda control computer for generating plasma in
accordance with preset processing conditions to sequentially apply plasma
processing to the workpieces held on said stage and also for sequentially
collecting system parameter values each of which represents a state of
the plasma processing,wherein said control computer is provided with:a
model-equation derivation unit for formulating a correlation of plural
parameter values, which indicate a state of said plasma processing
system, and outputting a model value of a system parameter of a
predetermined system,a record unit for storing, in every predetermined
period, a frequency that each of the collected system parameters of the
predetermined system deviates from a reference value set based on the
model value of the system parameter outputted by said model-equation
derivation unit,an occurrence rate calculation unit for calculating,
based on the frequency, an occurrence rate that the each of the system
parameter values deviates from the reference value,a comparison unit for
comparing the occurrence rate with a preset reference value to diagnose a
state of said system, anda display unit for showing a diagram
representing causal associations among respective system parameters of
the plasma processing system.

3. A plasma processing system comprising:a processing chamber provided
with a plasma generation unit for applying radio-frequency power to
supplied processing gas to generate plasma and a stage for holding
workpieces thereon, anda control computer for generating plasma in
accordance with preset processing conditions to sequentially apply plasma
processing to the workpieces held on said stage and also for sequentially
collecting system parameter values each of which represents a state of
the plasma processing,wherein said control computer is provided with:a
record unit for storing the collected system parameter values as
history,a statistical processing unit for calculating, based on the
history stored in said record unit, a mode value of a processing
parameter in a predetermined period, anda comparison unit for comparing
the mode value calculated by said statistical processing unit with a
preset reference value to diagnose a state of said system.

4. A plasma processing system comprising:a processing chamber provided
with a plasma generation unit for applying radio-frequency power to
supplied processing gas to generate plasma and a stage for holding
workpieces thereon, anda control computer for generating plasma in
accordance with preset processing conditions to sequentially apply plasma
processing to the workpieces held on said stage and also for sequentially
collecting system parameter values each of which represents a state of
the plasma processing,wherein said control computer is provided with:a
model-equation derivation unit for formulating a correlation of plural
parameter values, which indicate a state of said plasma processing
system, and outputting a model value of a predetermined system
parameter,a record unit for storing as history, in every predetermined
period, deviations of the collected system parameters from the model
value of the predetermined system parameter outputted by said
model-equation derivation unit,a statistical processing unit for
calculating, based on the history stored in said record unit, a mode
value of a deviation of the predetermined system parameter in a
predetermined period,a comparison unit for comparing the mode value
calculated by said statistical processing unit with a preset reference
value to diagnose a state of said system, anda display unit for showing a
diagram representing causal associations among respective system
parameters of the plasma processing system.

5. The plasma processing system according to claim 2 or claim 4, wherein
said display unit shows each system parameter value, which deviates from
its corresponding reference value, in a color different from system
parameter values which do not deviate from their corresponding reference
values.

6. The plasma processing system according to claim 4, wherein a maximum
value or minimum value is used in place of the mode value.

Description:

CROSS-REFERENCE TO RELATED APPLICATION

[0001]This application claims the priority of Japanese Patent Application
2009-096052 filed Apr. 10, 2009, which is incorporated herein by
reference.

BACKGROUND OF THE INVENTION

[0002]1. Field of the Invention

[0003]This invention relates to a plasma processing system, and especially
to a plasma processing system capable of diagnosing its state on the
basis of acquired parameter values.

[0004]2. Description of the Related Art

[0005]To form microcircuits or microelectron devices on a surface of a
semiconductor wafer or the like, plasma processing such as plasma etching
is used. As a high fabrication yield is required for a fabrication
process of semiconductor devices, there is an outstanding desire for a
technology that makes it possible to detect a sign before the occurrence
of a disastrous processing abnormality. In the event of occurrence of an
abnormality in a plasma processing system, it is also desired to achieve
restoration in a short time from the standpoint of improved fabrication
throughput.

[0006]As technologies for detecting a sign before the occurrence of a
disastrous processing abnormality, JP-A-2004-131777 discloses a method
that detects abnormal discharges of plasma and performs control of
workpieces on the basis of the frequency of the abnormal discharges.
JP-A-2004-200323 discloses a method that, when processing abnormalities
take place in succession, interrupts processing by estimating that a
plasma processing system is in a disastrously abnormal state. Further,
JP-A-2006-324316 discloses a method that collects system parameter values
of a plasma processing system and diagnoses that the plasma processing
system is abnormal if any system parameter value differs from the
corresponding system parameter value when the plasma processing system is
normal.

SUMMARY OF THE INVENTION

[0007]In plasma processing, however, a method that sets a distinct
threshold between an abnormality and a normality as in JP-A-2004-131777
generally does not work well, because fluctuations always exist in
processing conditions, thereby unavoidably resulting in such an erroneous
determination that normal processing may be determined to be abnormal or
abnormal processing may be determined to be normal.

[0008]Especially when an extremely minute foreign object is caught between
a workpiece and a stage on which the workpiece is held, an abnormal state
is detected in terms of a parameter of a processing system in many
instances although the processing itself is completed as normally. In
such a case, the processing system is determined to be abnormal although
the processing has been completed normally. The processing is hence
stopped, leading to a reduction in the operation rate of the system.

[0009]In view of such a drawback, JP-A-2004-200323 stops processing only
when processing abnormalities take place in succession. However, the
above-mentioned fluctuations mean the existence of such a situation that
after abnormal processing, the processing once becomes normal and then
becomes abnormal again. Therefore, a malfunction of the processing system
may be overlooked insofar as only successive abnormalities are detected
as abnormalities.

[0010]It is, therefore, a common practice to use the method that, as
disclosed in JP-A-2006-324316, collects processing parameters to
determine whether processing is abnormal or normal. Mere collection of
parameter values, however, cannot ascertain a cause of an abnormality in
many instances, because plural processing parameters generally turn out
to be abnormal values when a processing abnormality occurs. In such a
situation, the experience and intuition of a skilled engineer have to be
relied upon in many instances to ascertain the cause of the abnormality,
thereby making it difficult to take a quick countermeasure.

[0011]With these problems in view, the present invention has as an object
the provision of a plasma processing system which makes it possible to
detect the occurrence of an abnormality in the system with high accuracy
and further to readily search for a cause of the abnormality.

[0013]a processing chamber provided with a plasma generation unit for
applying radio-frequency power to supplied processing gas to generate
plasma and a stage for holding workpieces thereon, and

[0014]a control computer for generating plasma in accordance with preset
processing conditions to sequentially apply plasma processing to the
workpieces held on the stage and also for sequentially collecting system
parameter values each of which represents a state of the plasma
processing,

[0015]wherein the control computer is provided with:

[0016]a record unit for storing, in every predetermined period, a
frequency that each of the collected system parameter values deviates
from a preset reference value,

[0017]an occurrence rate calculation unit for calculating, based on the
frequency, an occurrence rate that the each of the system parameter
values deviates from the reference value, and

[0018]a comparison unit for comparing the occurrence rate with a preset
reference value to diagnose a state of the system.

[0019]Owing to the constitution described above, the plasma processing
system according to the present invention makes it possible to detect the
occurrence of an abnormality in the system with high accuracy and further
to readily search for a cause of the abnormality.

BRIEF DESCRIPTION OF THE DRAWINGS

[0020]FIG. 1 is a block diagram illustrating the construction of a plasma
processing system according to a first embodiment of the present
invention.

[0021]FIG. 2 is a block diagram illustrating details of a control computer
in the plasma processing system according to the first embodiment of the
present invention.

[0022]FIG. 3 is a block diagram illustrating the control computer of FIG.
2, which is additionally equipped with a model-equation derivation unit.

[0023]FIG. 4 is a diagram showing differences between a calculated value
and found values (experimental values) of a processing parameter.

[0024]FIG. 5 is a diagram showing occurrence rates of the determination of
an abnormality in predetermined periods.

[0025]FIG. 6 is an association diagram showing an illustrative output from
a schematization unit.

[0026]FIG. 7 is an association diagram showing an example in which a cause
of an abnormality in the system is diagnosed and visualized.

[0027]FIG. 8 is a diagram showing variations with time in a supply rate of
heat-conducting gas to be supplied to a stage.

[0028]FIG. 9 is a block diagram illustrating details of a control computer
in a plasma processing system according to a second embodiment of the
present invention.

[0029]FIG. 10 is a block diagram illustrating the control computer of FIG.
9, which is additionally equipped with a model-equation derivation unit.

[0030]FIG. 11 is a diagram showing variations with time in a mode value of
differences between a calculated value and found values (experimental
values) of a processing parameter.

[0031]FIG. 12 is a diagram showing variations with time in a supply rate
(found value) of heat-conducting gas and also variations with time in a
mode value of supply rates (found values) of the heat-conducting gas.

[0032]FIG. 13 is a diagram describing respective parameter names shown in
FIGS. 6 and 7 and their meanings.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

First Embodiment

[0033]The plasma processing system according to the first embodiment will
hereinafter be described with reference to FIGS. 1 through 8 of the
accompanying drawings. In FIG. 1, a plasma processing chamber 100 for
processing workpieces is provided with a gas supply unit 101 for
supplying processing gas, a valve 103 and gas exhaust unit 102 for
adjusting evacuation of the processing gas to control a pressure inside
the plasma processing chamber 100, and a pressure gauge 104 for measuring
the pressure within the plasma processing chamber 100. The plasma
processing chamber 100 is also provided with a plasma generation unit 106
for generating plasma, and the plasma generation unit 106 is provided
with a radio-frequency (hereinafter abbreviated as "RF") power source 109
for supplying power to the plasma generation unit 106 and a tuner 108 for
adjusting the impedance of a power supply line between the RF power
source 109 and the plasma generation unit 106.

[0034]Arranged inside the plasma processing chamber 100 is stage 105 for
holding a workpiece thereon. The stage 105 is provided with an RF power
source 111 for applying a voltage to the stage and a tuner 110 for
adjusting the impedance of a power supply line between the RF power
source 111 and the stage 105. It is to be noted that, when plasma is
generated by using electron cyclotron resonance, a coil is arranged as an
electromagnet around the plasma processing chamber 100.

[0035]The plasma processing system of this embodiment is also provided
with a control computer 112, and the control computer 112 is provided
with a processing parameter acquisition unit 113 for acquiring processing
parameters such as the indicated pressure value of the pressure gauge
104, the opening degree of the valve 103, the output power values of the
RF power sources 109,111, the impedance values and reflected power values
detected by the tuners 108,110.

[0036]Reference is next had to FIG. 2. As mentioned above, the control
computer 112 is provided with the processing parameter acquisition unit
113, and transmits received processing parameters to a schematization
unit 202, which schematizes causal associations among the processing
parameters, and also to a first comparison unit 203.

[0037]The schematization unit 202 schematizes the causal associations
among the processing parameters so received, and shows them on a display
unit 209. As a schematization method, a known method such as the SGS
algorithm, WL algorithm, PC algorithm, Dempster's covariance selection,
graphical modeling or multivariate analysis can be used.

[0038]The first comparison unit 203 determines whether or not a value of
each processing parameter deviates from a predetermined output range
(first reference value). The value of the processing parameter is
determined to be abnormal when it deviates from the first reference
value, but is determined to be normal when it does not deviate from the
first reference value.

[0039]The determination made by the first comparison unit 203 as described
above is stored as history in the record unit 204. Based on the history
stored in the record unit 204, an occurrence rate calculation unit 205
calculates an occurrence rate that the determination of an abnormal value
was made in a predetermined period.

[0040]The value of the occurrence rate, which has been calculated by the
occurrence rate calculation unit 205, is delivered to a second comparison
unit 206, and is compared with a predetermined second reference value to
determine whether or not the value of the occurrence rate is not smaller
than the second reference value. When the value of the occurrence rate is
not smaller than the second reference value, an alarm is given by an
alarm unit 207 to the effect that the plasma processing system is in an
abnormal state. In addition, the results of calculations by the control
computer 112 are shown on the external display unit 209.

[0041]A description will next be made about the predetermined output range
(first reference value) to be compared with each value of the processing
parameter at the first comparison unit. This output range is a range
indicating that the system is operating normally. It is, therefore,
desired to statistically determine the output range from the record of
previous processing data. Versatility will, however, be lost if the
output range is separately determined for respective different processing
conditions.

[0042]Referring to FIG. 3, a description will be made about the control
computer 112 additionally provided with a model-equation derivation unit
201 that produces standard values (model values) of the processing
parameters. The model-equation derivation unit 201 converts correlations
of the respective processing parameters into model equations such that
standard values can be produced for desired ones of the processing
parameters. When relations between values of desired one of the
processing parameters and values of the remaining processing parameters
are approximately expressed by a linear multivariable function, for
example, it is possible to calculate values (model values) of the
remaining processing parameters which the normal system can inherently
have relative to each value of the desired processing parameter.

[0043]As the ranges of normal values of the respective processing
parameters can be calculated by the control computer 112 as described
above, the reference values to be used at the first comparison unit 203
can be flexibly determined by using the ranges so that the versatility of
the system can be improved further.

[0044]The ranges of values of the respective processing parameters, which
the normal system can inherently have, can be determined, for example, by
statistically investigating the departures of found values of the
respective processing parameters from their corresponding model values.
Determination of the above-described reference ranges on the basis of the
thus-determined ranges is very convenient because desired conditions of
the normal system can be dealt with. It is to be noted that, although the
above description is directed to the method that approximately expresses
by the linear multivariable function the relations between values of the
desired one of the processing parameters and values of the remaining
processing parameters, the model equation for the relations may of course
be expressed by a different method which presumes a nonlinear function or
the like.

[0046]Based on the thus-received processing parameters, the model-equation
derivation unit 201 derives a model equation that expresses responses of
the desired processing parameter to the group of the remaining processing
parameters. The model-equation derivation unit 201 then transmits
response values (calculated values), which have been obtained by the
thus-derived model equation, to the first comparison unit 203. The first
comparison unit 203 compares each processing parameter (found value) so
received with its corresponding response value (calculated value)
obtained by the model equation, and calculates the difference between
them, the absolute value of the difference, the square of the difference,
or the like to determine the degree of a divergence of the processing
parameter value from its corresponding response value obtained by the
model equation. Subsequently, a determination is made based on the degree
of the divergence as to whether or not the processing parameter value
deviates from the corresponding response value obtained by the model
equation. The processing system is determined to be normal when the
processing parameter does not deviate, but is determined to be abnormal
when the processing parameter deviates.

[0047]The above-described determination made by the first comparison unit
203 is transmitted to the record unit 204, and the record unit 204 stores
the determination so received. Subsequent operations are the same as in
the case illustrated in FIG. 2.

[0048]The diagram of FIG. 4 shows the differences between the calculated
value of the desired processing parameter and its corresponding found
values (experimental values) as calculated by the first comparison unit
203. Relative to the overall number of processing steps plotted along the
abscissa, the differences between the calculated value of the desired
processing parameter and its corresponding found values, which are
plotted along the ordinate, behave substantially like white noise.

[0049]If a threshold is set (for example, a variance σmodel is
calculated with respect to the departures from the response value
obtained by the model equation and the threshold is set at
3σmodel) and a rule is made such that the state of the system
is diagnosed to be abnormal when the absolute value of the difference
between the calculated value and a found value of the processing
parameter exceeds the threshold, an alarm that the plasma processing
system is in an abnormal state is hence produced frequently. In such a
situation, a normal state is erroneously determined to be an abnormal
state, thereby not only lowering the operation rate of the system but
also impairing the reliability of the alarm. It is to be noted that, if
the threshold is set large, no abnormality can be detected even when the
plasma processing system falls in a truly abnormal state.

[0050]In the diagram of FIG. 5, occurrence rates that, in predetermined
periods (for example, during past 20 steps), a determination of
abnormality is made are plotted along the ordinate. Such a diagram is
obtained by the occurrence rate calculation unit 205. Since the
differences between a calculated value and found values of a processing
parameter are substantially like white noise as mentioned above, the rate
(%) that the determination of abnormality is made is low when the plasma
processing system is in a normal state. When the plasma processing system
falls in a truly abnormal state, however, the rate (%) that the
determination of abnormality is made increases. Accordingly, the
reliability of an alarm can be heightened. In FIG. 5, the system is
defined to be in a truly abnormal state when the rate (%) that the
determination of abnormality is made exceeds 60%. At this setting, it was
possible to detect, with high accuracy, each state that the system was in
a truly abnormal state. With respect to each of the remaining processing
parameters, similar processing is performed to determine whether the
plasma processing system is in a normal or abnormal state.

[0051]The association diagram of FIG. 6 illustrates an output from the
schematization unit 202 that outputs the causal associations among the
processing parameters. The processing parameters signs shown in FIG. 6
have the meanings summarized in FIG. 13. The arrows in FIG. 6 each
indicate that the tail is a cause and the head is an effect.

[0052]The association diagram of FIG. 7 illustrates an output from the
schematization unit 202 that outputs the causal associations among the
processing parameters. The processing parameters signs and arrows shown
in FIG. 7 have the same meanings as those shown in FIG. 6. In FIG. 7, the
processing parameters (F, O, P, I) that the differences between the
calculated values obtained by the model equation and their corresponding
found values exceeded their corresponding thresholds are highlighted by
hatching. In addition to the parameter (F), the found values of the other
parameters (O, P, I) each of which is in a causal association with the
parameter (F) deviate from their corresponding calculated values obtained
by the model equation, and are abnormal values. By tracing back the
causal associations, however, it can be readily estimated that the
parameter (F) (the opening degree of the valve 103) is the cause of the
abnormal state of the plasma processing system.

[0053]By schematizing the causal associations among the processing
parameters as described above, the cause of an abnormal state of the
plasma processing system can be readily estimated so that the maintenance
time can be shortened. It is also possible to facilitate the visual
recognition of the cause of the abnormal state by highlighting one or
more parameters, the found values of which deviated from the
corresponding reference ranges, in a color or pattern different from the
normal processing parameters as in FIG. 7.

[0054]As one example of abnormality detection, a description will be made
of an estimation method for the time of replacement of the stage 105. In
the plasma processing system, the workpiece is heated by plasma. A
cooling unit is, therefore, arranged inside the stage 105 for cooling the
workpiece 107. Upon cooling, heat-conducting gas having high thermal
conductive properties, such as helium, is filled between the workpiece
107 and the stage 105 to increase the thermal conductivity. When the
stage 105 and the workpiece 107 are in close contact with each other, the
heat-conducting gas practically does not leak out so that its supply rate
can be kept low. Once the surface of the stage 105 begins to wear off,
the heat-conducting gas leads out through the resulting clearance so that
the required supply rate of the gas increases. It is, therefore, possible
to recognize the wear conditions of the stage 105 by monitoring the
supply rate of the gas.

[0055]If an extremely minute foreign object is caught between the stage
105 and the work piece 107, the heat-conducting gas may leak out. In
other words, there is a situation that the required supply rate of the
heat-conducting gas increases even when the wearing of the stage 105 has
not progressed much.

[0056]The diagram of FIG. 8 shows variations with time of the supply rate
of heat-conducting gas to be supplied to the stage. It can be appreciated
that, as shown in the diagram, the actual value of the supply rate of the
heat-conducting gas increases as variations of the stage 105 progress
with time and the time for replacement of the stage 105 is approached. It
can also be observed that the supply rate occasionally undergoes a sudden
increase before the progress of variations of the stage 105. It is also
evident from the diagram that any attempt to detect the time for
replacement of the stage 105 by setting a threshold with respect to the
supply rate does not work well under such a situation.

[0057]When the occurrence rate of the found values greater than the preset
reference value is calculated, on the other hand, the results of the
calculation become similar to the curve shown in FIG. 8. When the
occurrence rate has exceeded 60% in this example, the time for
replacement can be readily notified by producing an alarm from the alarm
unit 207 such that the replacement of the stage 105 is urged.

[0058]As has been described above, the first embodiment of the present
invention calculates the occurrence rate of a situation that a collected
value of a system parameter deviates from the corresponding preset
reference range, and compares the thus-calculated occurrence rate with
its corresponding preset reference value to diagnose the state of the
system. It is, therefore, possible to produce a high-reliability alarm
for an abnormality of the system. Further, the use of the resulting
association diagram makes it possible to promptly find out the cause.

Second Embodiment

[0059]Referring next to FIGS. 9 through 12, a description will be made
about a control computer in the plasma processing system according to the
second embodiment will be described. As illustrated in FIG. 9, the
control computer 112 is provided with a processing parameter acquisition
unit 113 for receiving processing parameters, and transmits the
thus-acquired processing parameters to a schematization unit 202 for
schematizing causal associations among the processing parameters and also
to a record unit 204. At this time, the schematization unit 202
schematizes the causal associations among the received processing
parameters.

[0060]The record unit 204 stores the received values of each processing
parameter as history. The history, which the record unit 204 retains, is
read by a statistical processing unit 805, and a mode value of the
processing parameter in a predetermined period is calculated. At a second
comparison unit 206, the thus-calculated mode value is compared with its
corresponding preset reference value (second reference value). When the
mode value exceeds the reference value, the plasma processing system is
determined to be in an abnormal state so that an alarm is produced to an
operator by an alarm unit 207. In addition, these analytical results of
the control computer 112 are shown on a display unit 209.

[0061]The block diagram of FIG. 10 illustrates an example in which similar
to the first embodiment, a model-equation derivation unit 201 and a first
comparison unit 203 are arranged. In FIG. 10, the processing parameter
acquisition unit 113 transmits the acquired processing parameters to the
model-equation derivation unit 201, schematization unit 202 and first
comparison unit 203.

[0062]From the thus-received processing parameters, the model-equation
derivation unit 201 derives a model equation that expresses responses of
the group of the processing parameters other than desired one of the
processing parameters to the desired processing parameter. The
model-equation derivation unit 201 then transmits response values
(calculated values), which have been obtained by the thus-derived model
equation, to the first comparison unit 203. The first comparison unit 203
compares each processing parameter (found value) so received with its
corresponding response value (calculated value) obtained by the model
equation, and calculates the difference between them, the absolute value
of the difference, the square of the difference, or the like to determine
the degree of a divergence of the processing parameter value from its
corresponding response value obtained by the model equation.
Subsequently, a determination is made based on the degree of the
divergence as to whether or not the processing parameter value deviates
from the corresponding response value obtained by the model equation. The
processing system is determined to be normal when the processing
parameter does not deviate, but is determined to be abnormal when the
processing parameter deviates.

[0063]The above-described determination made by the first comparison unit
203 is transmitted to the record unit 204, and the record unit 204 stores
the thus-received determination as history. The history, which the record
unit 204 retains, is read by the statistical processing unit 805, and a
mode value of outputs from the first comparison unit 203 in the
predetermined period is calculated. Subsequent operations are the same as
in the case illustrated in FIG. 9.

[0064]The diagram of FIG. 11 shows variations with time of the mode value
of the difference between the calculated value of the desired processing
parameter and its corresponding found value as calculated by the first
comparison unit 203. Overall numbers of processing steps are plotted
along the abscissas, while mode values are plotted along the ordinate.
Compared with FIG. 4, the noise is reduced to facilitate the recognition
of the situation. This is attributed to the fact that the statistics
value of a mode value is a stable index having higher noise durability
compared with a statistics value such as an average.

[0065]The diagram of FIG. 12 shows variations with time in the supply rate
(found value) of heat-conducting gas to be supplied to a stage and
variations with time in mode value. It is appreciated that as shown in
FIG. 12, the use of a mode value makes it possible to ignore sudden
increases in the difference between a found value and its corresponding
calculated value and to exactly follow the trend of variations in the
difference.

[0066]Similar advantageous effects can also be brought about when a
minimum value is used in place of the above-described mode value. In the
case of a trend that the value of a desired processing parameter
progressively decreased over a predetermined period, similar advantageous
effects can also be brought about when a maximum value is used in place
of the mode value. Further, a statistics value such as a moving average
may also be used when noise is sufficiently small, or a statistics value
such as a variance or standard deviation may be used when it is desired
to deal with noise itself.

[0067]As has been described above, the second embodiment of the present
invention can produce a high-reliability alarm by using a statistical
index such as a mode value, maximum value or minimum value, thereby
making it possible to appropriately detect the time of occurrence of an
abnormality in the system.

Patent applications by Akira Kagoshima, Kudamatsu-Shi JP

Patent applications by Masaru Izawa, Tokyo JP

Patent applications in class With measuring, sensing, detection or process control means

Patent applications in all subclasses With measuring, sensing, detection or process control means